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A torus with a hole that can eat another torus. The transformation is continuous, and so can be achieved by stretching only without tearing or making new holes in the tori.

If W is a k-dimensional subspace of a vector space V with inner product <,>, then it is possible to project vectors from V to W. The most familiar projection is when W is the ...

The vertical perspective projection is a map projection that corresponds to the appearance of a globe when directly viewed from some distance away with the z-axis of the ...

where _3F_2(a,b,c;d,e;z) is a generalized hypergeometric function and Gamma(z) is the gamma function (Bailey 1935, p. 16; Koepf 1998, p. 32).

Whipple derived a great many identities for generalized hypergeometric functions, many of which are consequently known as Whipple's identities (transformations, etc.). Among ...

The q-analog of the binomial theorem (1-z)^n=1-nz+(n(n-1))/(1·2)z^2-(n(n-1)(n-2))/(1·2·3)z^3+... (1) is given by (1-z/(q^n))(1-z/(q^(n-1)))...(1-z/q) ...

The van der Grinten projection is a map projection given by the transformation x = (1) y = sgn(phi)(pi|PQ-Asqrt((A^2+1)(P^2+A^2)-Q^2)|)/(P^2+A^2), (2) where A = ...

A finite group G has a finite number of conjugacy classes and a finite number of distinct irreducible representations. The group character of a group representation is ...

Linear algebra is the study of linear sets of equations and their transformation properties. Linear algebra allows the analysis of rotations in space, least squares fitting, ...

A partial differential equation (PDE) is an equation involving functions and their partial derivatives; for example, the wave equation ...